At least in the US, that material included in what you're describing as the "Zeugnis" would often be considered a transcript (as opposed to what you're describing as an "Urkunde," which would typically be the diploma), but, while the transcript is an official document, it isn't usually very "fancy" -- more utilitarian.

Just for a start. I'm sure that others may have some better thoughts.

Ich habe in einem ähnlichen Fall (nach langer Recherche) Zeugnis (enthielt die Hauptnoten, wie Note für das gesamte Fachgebiet, Note der Bachelor-Arbeit und Gesamtnote des Abschlusses) mit Degree Certificate und Urkunde (keine Noten, nur Verleihung des Titels B.A.) mit Diploma übersetzt.

Diesen Dokumenten war allerdings noch ein drittes Dokument mit der Liste der Module samt Noten beigefügt, was in den USA das "transcript" ist.

In higher education (college/university), the courses taken and marks received are given in a transcript. (Zeugnis)

A diploma indicates the degree (e.g., BA) with the major.

I would see a certificate as being "less" than a diploma, i.e., for a specific course or program that is not a full post-secondary degree - possibly for a 3-month course or a refresher of some sort, for example.

Edit: report (card) would be used for elementary/high school.

At the university I attended courses and marks were always recorded in your academic transcript (sometimes referred to as an academic record). Oxford university also uses this terminology.

"A transcript is an official summary of your academic performance and progress to date."

Once a degree was conferred; you received a "degree" (a piece of paper) on which your name, the degree conferred, the conferring university and other relevant details appeared.